pdfCdfRank.m

% Compute the pdf, cdf and rank distributions for a sequence of numbers.
%
% INPUTS: sequence of values: x, (1xn), 'plt' - 'on' or 'off'
%         bin - bin size, default is [], then it gets selected
%         automatically
% OUTPUTS: pdf, cdf and rank distribution values, plot is optional
%
% Note: pdf = frequency distribution, cdf = cumulative frequency,
%       rank = log-log scale of the sorted sequence
% Last updated: November 24 2012

function [xpdf, ypdf, xcdf, ycdf, logk, logx] = pdfCdfRank(x, plt='off', bin = [])

    xx = unique(x);

    if length(bin) == 0;
        bin = length(xx) / 5;
    end

    for ii = 1:numel(xx)
        xcdf(ii) = xx(ii);
        ycdf(ii) = length(find(x <= xx(ii))) / numel(x);

        % how many x's fall in the interval [xx(ii)-0.5*numel(xx)/bin,xx(ii)+0.5*numel(xx)/bin]
        xpdf(ii) = xx(ii);
        ypdf(ii) = length(find(abs(xx(ii) - x) <= 0.5 * numel(xx) / bin)) / numel(x);
    end

    x=-sort(-x);
    logk = log(1:length(x));
    logx = log(x);

    if strcmp(plt, 'on')
        set(gcf, 'color', [1, 1, 1])

        subplot(2, 2, 1)
        hist(x, bin, 'facecolor', [0.5 0.5 0.5])
        title('histogram')

        subplot(2, 2, 3)
        plot(xpdf, ypdf, 'k.')
        title('pdf')
        axis('tight')

        subplot(2, 2, 2)
        plot(xcdf, ycdf, 'k.')
        title('cdf')
        axis('tight')

        subplot(2, 2, 4)
        plot(logk, logx, 'k.')
        title('rank')
        axis('tight')
    end


%!test
%!shared adj
%! adj = randomGraph(randi(30)+30,0.2);
%! [xp,yp,xc,yc,lk,lx] = pdfCdfRank(degrees(adj),'off');
%! assert(length(xp),length(xc))
%! assert(length(xp),length(yp))
%! assert(length(yp),length(yc))
%! assert(length(lk),length(lx))

%!test
%! [xp,yp,xc,yc,lk,lx] = pdfCdfRank(degrees(adj),'off', bin=5);
%! assert(length(xp),length(xc))
%! assert(length(xp),length(yp))
%! assert(length(yp),length(yc))
%! assert(length(lk),length(lx))

%!demo
%! adj = randomGraph(1000, 0.2);
%! pdfCdfRank(degrees(adj),'on');